Detecting and estimating coherence based on coherence witnesses

Abstract

Quantum coherence has wide-ranging applications from quantum thermodynamics to quantum metrology, quantum channel discrimination and even quantum biology. Thus, detecting and quantifying coherence are two fundamental problems in quantum resource theory. Here, we introduce feasible methods to detect and estimate the coherence by constructing coherence witnesses for any finite-dimensional states. Our coherence witnesses detect coherent states by testing whether the expectation value of the witness is negative or not. Two typical coherence witnesses are proposed and discussed based on our witness-constructing method, which are also used to estimate the robustness of coherence, $l_1$-norm and $l_2$-norm of coherence measures. Furthermore, we compare one of our coherence witness with a previously introduced witness, by proving that our witness is strictly stronger than that previous witness. We also present an application of coherence in a quantum metrology task, in which we estimate an unknown parameter by measuring our coherence witness.

7 pages, 2 figures

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Cited by in corpus (13)

• Universal Method to Estimate Quantum Coherence
• Skew information-based coherence generating power of quantum channels
• Factorization dynamics between quantum Fisher information and quantum coherence
• Genuine non-Gaussian entanglement of light and quantum coherence for an atom from noisy multiphoton spin-boson interactions
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• Witnessing quantum coherence with prior knowledge of observables
• Detecting coherence with respect to general quantum measurements
• The tightness of multipartite coherence from spectrum estimation
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• Classifying coherence with a finite set of witnesses